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Lyapunov-like conditions for prescribed-time stability of perturbed impulsive systems

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  • Mapui, Arnab
  • Mukhopadhyay, Santwana

Abstract

The present work deals with the problem of prescribed-time control of non-linear impulsive systems consisting of external perturbations. Lyapunov-like sufficient conditions for prescribed-time and practical prescribed-time stability are provided for vanishing and non-vanishing perturbations, respectively. Depending on the user's requirements, some sequences of stabilizing impulses are constructed in this regard. It is shown that the systems consisting of vanishing-type disturbances can attain prescribed-time stabilization at the origin. On the other hand, in the presence of non-vanishing disturbances, which can consist of bounded or unbounded disturbances, the trajectories of the system can enter a stable region only within the prescribed time. Moreover, the stable region is independent of the impulsive strength and the prescribed-time. The efficacy of the proposed results is provided through various examples and their numerical simulations.

Suggested Citation

  • Mapui, Arnab & Mukhopadhyay, Santwana, 2025. "Lyapunov-like conditions for prescribed-time stability of perturbed impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006489
    DOI: 10.1016/j.amc.2024.129187
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    References listed on IDEAS

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    1. Cheng, Mengqing & Zhao, Junsheng & Xie, Xiangpeng & Sun, Zong-yao, 2024. "A novel finite-time stability criteria and controller design for nonlinear impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    2. Shuai Liu & Chuan Chen & Haipeng Peng, 2020. "Fixed-Time Synchronization of Neural Networks with Discrete Delay," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, August.
    3. Xing, Ying & He, Xinyi & Li, Xiaodi, 2023. "Lyapunov conditions for finite-time stability of disturbed nonlinear impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 440(C).
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